SAFER: Surface-Adaptive Feature Fields for Cross-Source Point Cloud Registration

Point clouds captured by heterogeneous LiDAR sensors exhibit divergent sampling patterns and densities, causing the same physical surfaces to be observed at shifted and non-uniform locations. Existing methods typically encode local geometry with superpoints and their sampled neighborhoods, which can entangle stable surface structure with sensor-dependent sampling variation. Consequently, representations may vary with the sensing mechanism, even when the underlying physical geometry is unchanged. To address this, we propose SAFER, a cross-source point cloud registration framework that lifts superpoint features into a continuous, surface-adaptive feature field by assigning each superpoint an anisotropic Gaussian basis in its local tangent-normal frame. The resulting normalized field affinity provides a geometry-aware prior that encourages compatible support interactions while down-weighting geometrically inconsistent neighborhoods. With this prior, we design Field-Aware Geometric Attention to guide contextual aggregation and introduce a Kernel-Guided Feature Adapter to perform kernel-conditioned descriptor refinement. An overlap-aware field objective further maximizes the consistency of ground-truth-aligned feature fields within their mutually observable regions. To alleviate the scarcity of large-scale cross-source data, we construct two benchmarks. Forest Cross-Source comprises ground-to-aerial LiDAR pairs in unstructured forest scenes, while Indoor Multi-LiDAR covers heterogeneous spinning and solid-state LiDARs in indoor environments. Extensive experiments demonstrate that SAFER improves registration performance across diverse sensor configurations, with notable benefits under severe sampling discrepancies.